Which of the following numbers is a multiple of 14? ${42,46,54,62,97}$
Explanation: The multiples of $14$ are $14$ $28$ $42$ $56$ ..... In general, any number that leaves no remainder when divided by $14$ is considered a multiple of $14$ We can start by dividing each of our answer choices by $14$ $42 \div 14 = 3$ $46 \div 14 = 3\text{ R }4$ $54 \div 14 = 3\text{ R }12$ $62 \div 14 = 4\text{ R }6$ $97 \div 14 = 6\text{ R }13$ The only answer choice that leaves no remainder after the division is $42$ $ 3$ $14$ $42$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $14$ are contained within the prime factors of $42$ $42 = 2\times3\times7 14 = 2\times7$ Therefore the only multiple of $14$ out of our choices is $42$. We can say that $42$ is divisible by $14$.